The company has spent billions of dollars in deals in the past years, ballooning its debt to $26.6 billion, more than half of its current market value.

"It is time for Allergan's management to concentrate on running a world class pharmaceutical and aesthetics business and forego thoughts of, or the exhilaration from, an ambitious acquisition strategy," the shareholders said in a letter.

Billionaire investor David Tepper's Appaloosa and Senator Investment, led by Douglas Silverman, together hold a nearly 2 percent stake in the company.

The stock rose as much as 2.5 percent on Tuesday, before paring some of its gains to trade up 1 percent at $151.95 in late-afternoon trading. They have fallen about 33 percent in the past 12 months.

The Dublin-based company decided to sell its women's health and infectious disease businesses last week, an outcome of a strategic review that the company had undertaken under CEO Brent Saunders earlier this year.

However, some investors had hoped for more dramatic actions from the review.

"Like the rest of the investment community, we were underwhelmed by the company's half-hearted attempt to restore strategic momentum," Appaloosa's Tepper and Senator Investment's Silverman said.

In response, Allergan said the conclusion of its strategic review was to pursue a disciplined capital allocation strategy.

The hedge funds said the company should hire a new person for one of the posts from outside the company after splitting the position.

They also asked the company to replace two additional directors on the company's board.

Allergan said it remained active and aggressive in board refreshment, pointing to three recent director appointments in the past 16 months.

The shareholders said they had previously sent similar letters to the drugmaker's board in April and May.

In May, Appaloosa received Federal Trade Commission's anti-trust clearance to become an activist investor in Allergan.

(Reporting by Manas Mishra in Bengaluru; Editing by Arun Koyyur)

By Manas Mishra